Terse report on the fit of one or more spatially explicit capture--recapture models. Models with smaller values of AIC (Akaike's Information Criterion) are preferred. Extraction ([) and logLik methods are included.
# S3 method for secr
AIC(object, ..., sort = TRUE, k = 2, dmax = 10, criterion = c("AICc","AIC"))
# S3 method for secrlist
AIC(object, ..., sort = TRUE, k = 2, dmax = 10, criterion = c("AICc","AIC"))
# S3 method for secr
logLik(object, ...)
secrlist(...)
# S3 method for secrlist
[(x, i)
secr
object output from the function
secr.fit
, or a list of such objects with class c("list","secrlist") secr
objects criterion
:
logLik.secr
returns an object of class `logLik' that has
attribute df
(degrees of freedom = number of estimated
parameters).
Models to be compared must have been fitted to the same data and use the same likelihood method (full vs conditional).
AIC with small sample adjustment is given by
$$ \mbox{AIC}_c = -2\log(L(\hat{\theta})) + 2K + \frac{2K(K+1)}{n-K-1} $$
where \(K\) is the number of "beta" parameters estimated. The sample size
\(n\) is the number of individuals observed at least once (i.e. the
number of rows in capthist
).
Model weights are calculated as $$w_i = \frac{\exp(-\Delta_i / 2)}{ \sum{\exp(-\Delta_i / 2)}}$$, where \(\Delta\) refers to differences in AIC or AICc depending on the argument `criterion'.
Models for which delta > dmax
are given a weight of zero and are
excluded from the summation. Model weights may be used to form
model-averaged estimates of real or beta parameters with
model.average
(see also Buckland et al. 1997, Burnham and
Anderson 2002).
The argument k
is included for consistency with the generic method AIC
.
secrlist
forms a list of fitted models (an object of class
`secrlist') from the fitted models in …. Arguments may include
secrlists. If secr components are named the model names will be retained
(see Examples).
Buckland S. T., Burnham K. P. and Augustin, N. H. (1997) Model selection: an integral part of inference. Biometrics 53, 603--618.
Burnham, K. P. and Anderson, D. R. (2002) Model Selection and Multimodel Inference: A Practical Information-Theoretic Approach. Second edition. New York: Springer-Verlag.
Hurvich, C. M. and Tsai, C. L. (1989) Regression and time series model selection in small samples. Biometrika 76, 297--307.
Turek, D. and Fletcher, D. (2012) Model-averaged Wald confidence intervals. Computational statistics and data analysis 56, 2809--2815.
model.average
, AIC
, secr.fit
, print.secr
, score.test
, LR.test
, deviance.secr
## Compare two models fitted previously
## secrdemo.0 is a null model
## secrdemo.b has a learned trap response
AIC(secrdemo.0, secrdemo.b)
## Form secrlist and pass to AIC.secr
temp <- secrlist(null = secrdemo.0, learnedresponse = secrdemo.b)
AIC(temp)
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